When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
The Pedunculopontine Nucleus (PPN) is a group of neurons located in the brainstem, specifically in the pontine region. Here is an overview of the Pedunculopontine Nucleus: 1. Anatomy : o The PPN is situated in the rostral part of the brainstem, near the junction of the pons and midbrain. It is part of the reticular formation, a network of neurons involved in various physiological functions. o The PPN receives inputs from multiple brain regions, including the basal ganglia, thalamus, and cortex, and sends outputs to structures involved in motor control, arousal, and gait. 2. Function : o Motor Control: The PPN is implicated in the regulation of motor functions, particularly in the control of posture, locomotion, and movement initiation. It is involved in coordinating rhythmic movements and adjusting gait patterns. o Arousal and Attention: The PPN is also associated with arousal, wakefulness, and attention. It plays a role in regulat...